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Ordinary Differential Equations [PDF]

Technometrics, 1975
Many problems of higher analysis presuppose a knowledge of ordinary differential equations; for example, problems of potential theory, of the calculus of variations, of theoretical physics and of partial differential equations (see Chapter 37.). Beyond this, a wide field of applications is opened up by ordinary differential equations; for example, the ...
W. Gellert, H. Küstner, H. Kästner, S. Gottwald, M. Hellwich   +4 more
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Ordinary Differential Equations [PDF]

, 2009
In this chapter we will introduce some notions and methods related to ordinary differential equations (ode). We study different representations of the solutions to odes, the singular points and the plane phases of planar odes, and an example of an ode with five equilibrium points.
Tsuneyoshi Nakayama, Hiroyuki Shima
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Ordinary Differential Equations

The American Mathematical Monthly, 1971
When the derivative y’ = f’(t) of an unknown function y = f(t) is given, we usually have to find the antiderivative. We treated this problem in Sections 9.3 and 9.5. Sometimes the derivative y’ is not given as a function of t, but is involved in an equation which contains also the unknown function y = f(t). As an example, consider the equation $$y'
Ray Redheffer, Jack K. Hale
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Ordinary Differential Equations [PDF]

, 1980
Many problems in applied mathematics lead to ordinary differential equations. In the simplest case one seeks a differentiable function y = y(x) of one real variable x, whose derivative y′(x) is to satisfy an equation of the form y′(x) = f(x, y(x)), or more briefly, $$y' = f\left( {x,y} \right)$$ (7.0.1) one then speaks of an ordinary ...
J. Stoer, R. Bulirsch
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Ordinary Differential Equations

2012
In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice.
Claudia Valls, Luis Barreira
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Ordinary Differential Equations

2016
The ordinary differential equations (ODE ’s in short), or simply differential equations (DE ), are the equations of the type $$\displaystyle{F\left (x,y,y^{{\prime}},y^{{\prime\prime}},\ldots,y^{(n)}\right ) = 0,}$$ relating the variable x, a function y(x) of x, and its derivatives \(\frac{\text{d}y} {\text{d}x} = y^{{\prime}}\), \(\frac{\text{d}
Thomas Zeugmann, Werner Römisch
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Ordinary differential equations

2010
A differential equation is an equation involving one or more derivatives of an unknown function. If all derivatives are taken with respect to a single independent variable we call it an ordinary differential equation, whereas we have a partial differential equation when partial derivatives are present.
Fausto Saleri, Alfio Quarteroni, Alfio Quarteroni, Paola Gervasio   +3 more
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Ordinary Differential Equations

1994
Dynamical systems are often expressed in terms of ordinary differential equations. An example are the canonical equations of motion in Hamiltonian systems $${\dot p_i} = - \frac{{\partial H}}{{\partial {q_i}}},\;{\dot p_i} = \frac{{\partial H}}{{\partial {q_i}}},$$ (12.1) where the time derivatives of the canonical coordinates and momenta are
H.-J. Jodl, H. J. Korsch
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Explicit Ordinary Differential Equations [PDF]

, 1998
In the last chapter we discussed the numerical treatment of explicit ordinary differential equations. Here, we will consider the more general case, implicit ordinary differential equations.
Edda Eich-Soellner, Claus Führer
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